Section 1: Model Description and Implementation                       

Section 1: Model Description and Implementation

Our model features groups of actors, interlinked by a network of social relationships, who develop and search for valuable ideas. An overview of the model is provided in the main text. In this appendix we provide additional details on the implementation of the primary model elements and walk through a sample run of the model. The model was built and simulated in the widely used NetLogo Agent-Based Modeling Environment (Wilensky, 1999). The code to implement the NK performance landscape was adapted from an implementation of the model used in Lazer & Friedman (2007) written by Joshua Becker, who we thank for making publicly available in the NetLogo Modeling Commons (“Problem Solving in Networks”, https://modelingcommons.org/browse/one_model/5219).

Primary Model Elements

The model contains five primary elements: ideas, performance landscapes, actors, a social network, and change events.

  1. Ideas. Ideas are comprised of multiple features that jointly determine the value of a given idea to the organization. We capture these properties in our model by representing ideas on a N-dimensional idea space, in which each dimension corresponds to a particular feature of an idea, and each feature can have one of two states. Ideas are represented by a N-digit bit string where each digit denotes the state of its corresponding feature, on (1) or off (0).

    We also created an option to run the model with a custom, multilevel representation for ideas that enabled us to visualize the model in low dimensions without losing the complexity we desired in the problem space. At the high level of the custom option, ideas are defined by their location in a two-dimensional feature space. Each dimension contains 32, instead of 2, states which are denoted by discrete integer values. At a low level, each combination of features also corresponds to a 10-digit bit string representation of the integer location, which can be thought of as containing more detailed information on the elements of each idea. The bit string is a concatenation of the binary representations of the integers. For example, the 5-digit binary representation of the integer 17 is 10001, and for the integer 25 it is 11001. The 10-digit bit string representation for the location {17, 25} would therefore be 1000111001. The low-level bit string representation is used to recombine ideas in the same way as the non-custom representation of ideas; the high-level integer representation of an idea’s location the feature space is used to determine its performance through a “custom landscape” described below.

  2. Performance Landscapes. The performance landscape maps the feature space location of an idea to the performance scores for that idea. A key characteristic of the types of performance landscapes we use in this model is that the impact of a particular value of one dimension of the feature space on performance depends on the value of the other. The more complex the problem (i.e., the more interdependencies matter for performance), the greater the number of peaks and valleys in the landscape; therefore, the easier it is to get stuck at local optima and not find the highest performing location (Levinthal, 1997). Each peak in the landscape has a unique basin of attraction, which is defined as the set of all locations that would lead to that peak if actors could engage only in self-search that always chose the adjacent location with the maximum performance. The basin of attraction for the peak with the highest performance we consider “the last mile.”

    Performance landscapes were generated using two broad approaches. The first follows the common “NK landscape” approach used in the computational strategy and organizations literature, where N represents the number of dimensions in idea space and K the degree of interdependence between those dimensions (Levinthal, 1997; Lazar & Friedman, 2007; Lenox, Rockart, & Lewin, 2007). Each feature, f, makes a contribution to performance, cf. cf itself is comprised of multiple components. The number of components in cf is determined by the number of other features on which f depends, K, and the number of states possible for each feature – one component is included for every possible combination of states among the interconnected features. cf is calculated by summing the performance value of each of its constituent components. The performance value of an entire solution is determined by averaging across all cf. In our implementation, the K other features to which f was connected were selected at random, and the performance value of each component within cf was determined by a random draw from a uniform distribution ranging from 1 to 1000. A new NK landscape was generated for each run of the model. An overview of their mean characteristics is provided in Table OA1.

    The second approach was used only with our “custom” idea representation. When the custom option was used, we generated a new performance landscape for each run by picking five percent of the locations as starting points for diffusing performance to surrounding areas, and one additional location as a clear global peak. Figure 1a in the main text depicts a representative custom landscape. On average, the custom landscapes used in the model contained 9.6 total peaks (ranging from 5 to 15), and the highest peak of a landscape featured the level of idea performance that was 3.5 times as high as that of the second highest peak.

Table OA1. Characteristics of Performance Landscapes Used in Model

Mean value from 5000 runs of the model

Landscape

Number of solutions

Local peaks (number)

Local peaks (% of solutions)

Size of the last mile (% of solutions)

Reaching Global Peak (% of focal action chains)

Custom Landscape

1,024

9.61

0.94

10.82

17.06

NK Landscape, N=8, K=2

256

5.21

2.03

48.07

36.56

NK Landscape, N=8, K=4

256

10.43

4.07

27.67

22.18

NK Landscape, N=8, K=6

256

19.70

7.70

13.99

12.48

NK Landscape, N=10, K=2

1,024

7.65

0.75

44.08

32.50

NK Landscape, N=10, K=4

1,024

18.32

1.79

23.13

19.24

NK Landscape, N=10, K=6

1,024

37.67

3.68

11.19

11.02

NK Landscape, N=12, K=2

4,096

11.89

0.29

39.76

29.34

NK Landscape, N=12, K=4

4,096

32.44

0.79

19.50

17.72

NK Landscape, N=12, K=6

4,096

75.95

1.85

8.65

9.50

  1. Actors. Actors hold a belief about what location in the idea space yields the highest performance. An actor can update their current belief with a higher performing belief in one of three ways. First, they can search the areas of the idea space that are adjacent to their current belief on their own (self-search). For NK landscapes, adjacent is defined by all the solutions that result from switching the state of a single feature from 0 to 1, or vice versa. For the custom landscapes, adjacent is defined as one of a solutions eight neighbors on the solution grid. The actors self-search behavior is governed by a parameter called ss-max that equaled true when actors picked the maximum performing adjacent solution when engaged in self-search, and false when actors randomly picked any better performing adjacent solution. In all cases, the solution picked had to be higher performing than their existing solution. Second, they can copy a higher performing belief from a network contact (transfer). Third, they can recombine elements of their current belief with those of a network contact.

    Actors are also characterized by two general tendencies that drive the actions happening in a model iteration (see Figure OA1). One tendency, collab, is an actor’s tendency to collaborate with others. It governs the frequency with which the actor attempts to engage in collaboration (i.e., recombination or copying) as opposed to searching on their own. The second tendency, recomb, is the tendency to innovate when working with others. It governs the frequency with which the actor attempts to engage in recombination instead of copying, given that an actor has engaged in collaboration. In the results presented in the main text, the values of collab and recomb for a specific actor were determined by taking a random draw from a normal distribution with a mean 0.8 and standard deviation of 0.1. This implies that the expected probability that self-search occurs in any given round is 0.2, and the expected probability of having two actors willing to collaborate is (0.8)×(0.8) = 0.64. By the same token, since recomb is set to 0.8, it implies that the expected probability that two actors engage in a recombination interaction in any given round is P(interaction)×recomb×recomb = (0.64)×(0.8)×(0.8) = 0.4096. Similarly, the expected probability that a transfer occurs in any given round is (0.64)×(0.2) = 0.128. Note that engaging in a search or interaction activity of any type does not mean that either actor changed his or her belief. Beliefs are updated only if a better-performing idea is developed or found. Our boundary condition analyses, reported in the main text, explore the sensitivity of our results to varying the mean levels of collab and recomb.

Figure OA1. Description of a Model Iteration

Notes: Ego is the actor randomly selected to act in a given iteration, while alter corresponds to any connected actor that ego chooses to collaborate with. Paremeters collabi and collabj represent ego’s and alter’s propensities to collaborate, respectively, while recombi and recombj represent ego’s and alter’s propensities to recombine, respectively.

  1. Social network. A social network of collegial ties governs the interactions between actors and the possible transfers and recombinations. We used one of five different network conditions to generate a network at initialization. Three of at the network conditions generated small-world networks with 45 total edges as described in the main text, wherein 25 actors were distributed into 5 tightly interconnected network communities that were only sparsely interconnected to each other (SW1, SW2, SW3, Figure 2); the “random” network condition generated networks that randomly assigned the same number of edges between workers; and the “fully connected” condition where all workers were connected to all other workers. Conditions SW2, SW3, and “random” involved random rewiring of edges, resulting in the generation of a range of networks with similar properties. Conditions SW1 and “fully connected” involved no rewiring so they resulted in exactly the same network structure every time.

    The social network also governed the initialization of beliefs. Network communities were randomly assigned a different point in the feature space. Actors within a network community were then randomly assigned a location on or near that point. Consequently, actors hold ideas much more similar to others within their network community than to those outside their network community when the simulation begins. The only restriction on the point that served as the centroid for the network community was it could not be a location from which an actor could find the global peak through only self-search. (Relaxing this restriction did not change the primary results of the model. See Section 6, Online Appendix.) That restriction did not apply to the actor randomly chosen to be the actor holding the “focal idea” and randomly relocated in time period 1.

    Figure OA2 displays the distribution of small world quotients across 100 initializations of each network in our study.

Figure OA2. Distribution of Small World Quotient Across Networks Used in Experiment

Notes: Y-axis is the small world quotient, defined as the ration (C/CR)/( L/LR), where C is the clustering coefficient for the observed network; CR the clustering coefficient of a random network of the same size and connectivity; L, the average path length for the observed network; and LR the average path length of the corresponding random network.

  1. Change events. Actors interacting within the social network produce five different types of change events as a consequence of updating their current beliefs: (1) Self-search: actor learned about the newly adopted idea through independent search of adjacent solutions; (2) Within-network-community transfer: actor copied an idea from another member of her own network community; (3) Between-network-community transfer: actor copied an idea from a member of a different network community; (4) Within-network-community recombination: actor developed the idea through a recombination with another member of her own network community; (5) Between-network-community recombination: actor developed the idea through a recombination with a member of a different network community.

    Recombination, whether between or within a network community, occurs through single-point genetic crossover of the bit string representations of their beliefs (Holland and Order, 1995). The genetic crossover process yields a new location in feature space, whose performance each actor independently evaluates. Regardless of the type of attempted improvement, if the new location discovered is higher performing, an actor will update her belief. Single-point genetic crossover is accomplished by picking a random point between two digits, where each string gets “cut,” creating two pieces—left and right—for each actor. The left half of Actor A’s string is then concatenated with the right half of Actor B’s, and the right half of Actor A’s string is paired with the left half of Actor B’s to create two novel bit strings. We randomly selected one of the two bit strings produced for evaluation by the actors.

    For example, consider the case where custom landscape is used; Actor A’s current belief for the highest performing location in feature space is {17, 25}, which corresponds to a bit string representation of 1000111001; Actor B’s current belief is location {28, 30}, which corresponds to a bit string representation of 1110011110. Further assume that the model chose a cut point between digits 6 and 7. Crossover in this case would yield the following two new strings 1000111110 and 1110011001. One of those two strings is then randomly selected (e.g., 1000111110), reconverted into the corresponding integer values in the feature space {28, 25}, and presented to both actors who independently compare the single outcome to their current belief. Recombination works in the exact same way when NK landscapes are used. The only difference is that the ideas are already represented as bit strings, so conversation from a spatial location to bit string is not necessary.

Sample Run of the Model

Please refer to the description of model steps in the main text as well as Figure OA1. Figure OA3(a-c) below provides three snapshots of a representative run of the model at time steps 0, 200, and 1000, using the “custom landscape” option so that it can be visualized. The cells of the grid represent the space of idea features. Each location on the grid (idea) is associated with a specific level of performance determined by the underlying performance landscape. On this performance landscape, lighter colors indicate higher-performing ideas; darker colors represent lower-performing ideas. The performance landscape is rugged, which is representative of complex problems, where idea features interact to determine performance. The ruggedness is evident in the lighter areas—which represent local performance peaks—being surrounded by darker valleys of lower-performing ideas. The bright white spot in the lower right corner is the global peak, indicating the best possible idea that can be discovered in the focal run of the model.

The social network of the collective features 25 white nodes, which represent actors who are interconnected by 45 white information-sharing relationships. The network is described by a small-world network topology with five densely interconnected network communities that are only sparsely connected across communities (Figure OA3). Importantly, the actors are placed on the location of the idea feature landscape in the way that corresponds to their initially held beliefs about the best-performing idea. As Figure OA3(a) illustrates, at t=0, actors vary in their initial beliefs about which combination of idea features constitutes the best-performing idea, no actor is on the global peak, and actors in the same network community are more similar to one another in their initial beliefs than to the actors located in other network communities.

As actors begin to interact with one another or engage in self-search, they progress in finding better-performing ideas, and begin to make their way toward higher-performing (lighter) locations on the idea feature grid. See Figures OA3(b) and OA3(c). Regardless of the type of search in which the actors engage, some of the actors will inevitably end up converging on the same ideas. Such convergence may result from actors’ acquiring one another’s ideas through transfer or from actors jointly developing a new idea through recombination that is higher performing than either of their current ideas, with both subsequently adopting it. Yet another possibility is that actors can converge on the same idea through self-search, especially if their ideas happen to be in the same basin attraction and thus tend toward the same peak.

Figure OA3. Illustrative Model Run

Notes: In this run, the number of unique beliefs has decreased from 20 in time period 0 to 12 by time period 200. By time period 1000, the actors have converged on four unique ideas, each of which is associated with a different local peak on the performance landscape. In this particular case, no actor has discovered the best possible idea, as evidenced in the global peak (bright white cell in the bottom right corner) remaining unoccupied.

Section 2: Supplementary Results by Network                            

Section 2: Supplementary Results by Network

Table OA2. Expected percentage point change in the probability of a given action chain reaching the last mile and developing into the best idea corresponding to one additional change activity, by Social Network and ss-max.

Actor chooses max performing idea
(ss-max = TRUE)

Actor chooses better performing idea
(ss-max = FALSE)

Small World I

Small World II

Small World III

Random

Fully-Connected

Small World I

Small World II

Small World III

Random

Fully-Connected

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

Within-network-community recombination

1.97

-8.00

1.79

-8.51

1.83

-6.95

0.58

-2.60

0.78

-2.85

0.61

-2.74

Between-network-community recombination

3.43

-6.10

2.29

-5.98

2.25

-5.04

1.79

-1.23

1.10

-1.66

0.98

-1.96

Within-network-community transfer

-0.61

-0.40ns

-0.69

0.62ns

-0.50

0.08ns

-0.55

0.19ns

-0.39

0.85

-0.30

0.85

Between-network-community transfer

0.73

4.63

0.47

4.68

-0.12ns

4.10

0.64

5.19

-0.15ns

3.63

-0.11ns

3.00

Self-search

-1.18

17.01

-1.09

17.05

-1.16

16.76

-0.83

16.85

-0.76

15.84

-0.25

8.00

-0.37

7.36

-0.25

7.13

-0.25

7.81

-0.18

6.93

Recombination

1.52

-6.21

0.96

-4.45

0.67

-2.06

0.36

-1.48

Transfer

-0.31

2.23

-0.11

1.79

-0.15

0.94

-0.03ns

1.14

No. of observations (chains)

36,905

16,921

37,029

17,273

36,956

17,515

37,127

17,203

37,184

18,968

37,007

20,147

37,111

20,309

36,989

20,782

36,995

20,295

37,075

22,059

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level

Probability changes calculated for the median observation using logistic regressions. 'Entered Last Mile' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. 'Reached Best Idea' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Recombinations and transfers cannot be disaggregated by between- and within-network community in random and fully-connected networks because these network structures do not have network communities.

Estimations made using data from 50,000 runs for each network and ss-max condition (5,000 runs by lanscape). All runs used parameters collab = 0.8 and recomb = 0.8.




Section 3: Supplementary Results by Landscape                         

Section 3: Supplementary Results by Landscape

Table OA3. Expected percentage point change in the probability of a given action chain reaching the last mile and developing into the best idea corresponding to one additional change activity, by Landscape and ss-max.


Actor chooses max performing idea
(ss-max = TRUE)

Custom landscape

N=8, K=2

N=8, K=4

N=8, K=6

N=10, K=2

N=10, K=4

N=10, K=6

N=12, K=2

N=12, K=4

N=12, K=6

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

Within-network-community recombination

1.14

-6.39

2.88

-5.25

3.91

-9.85

3.35

-9.23

2.02

-6.32

2.30

-8.44

2.18

-8.68

1.44

-4.71

1.70

-6.33

1.47

-10.14

Between-network-community recombination

2.49

-2.72

3.35

-5.88

4.37

-4.44

3.14

-10.99

2.73

-5.50

2.93

-5.73

2.15

-9.51

2.90

-2.94

2.60

-3.95

2.03

-6.41

Within-network-community transfer

-0.45

0.39ns

-1.09

1.35

-0.72

1.53ns

-0.74

-1.55ns

-0.73

0.62ns

-0.73

0.23ns

-0.54

0.46ns

-0.58

-1.02ns

-0.46

-1.00ns

-0.47

-0.64ns

Between-network-community transfer

0.92

3.05

-0.08ns

3.94

-1.10

0.94ns

-0.62ns

1.13ns

0.45ns

4.63

0.12ns

3.39

0.11ns

1.40ns

0.63ns

3.69

0.55

5.04

0.36

0.22ns

Self-search

-1.06

8.03

-1.79

14.81

-2.29

30.79

-1.93

22.28

-1.53

19.48

-1.53

19.48

-1.29

26.10

-1.29

14.97

-1.26

16.92

-0.90

19.98

No. of observations (chains)

21,741

6,324

12,677

13,922

17,793

9,155

21,577

4,832

13,763

13,449

18,890

8,515

21,996

4,652

14,718

13,066

19,677

8,149

22,645

4,024

Actor chooses better performing idea
(ss-max = FALSE)

Custom landscape

N=8, K=2

N=8, K=4

N=8, K=6

N=10, K=2

N=10, K=4

N=10, K=6

N=12, K=2

N=12, K=4

N=12, K=6

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

(34)

(35)

(36)

(37)

(38)

(39)

(40)

Within-network-community recombination

0.77

-3.28

0.55

-3.03

1.33

-3.86

1.36

-5.44

0.13ns

-1.59

0.37

-1.75

0.77

-1.62

0.21ns

-1.30

0.35

-1.97

0.69

-1.97

Between-network-community recombination

2.64

-1.52

0.51ns

-1.74

0.94

-1.86

1.44

-0.59ns

0.47

-1.81

0.97

-0.92ns

1.11

-1.24ns

0.77

-1.37

0.86

-0.51ns

1.14

-1.70

Within-network-community transfer

-0.35

0.53ns

-0.95

1.10

-1.01

1.02ns

-0.79

0.74ns

-0.38

0.19ns

-0.33

-0.22ns

-0.76

0.45ns

-0.45

0.70

-0.28

0.05ns

-0.37

0.99ns

Between-network-community transfer

0.96

6.24

-0.28ns

3.65

-0.94

2.07ns

0.07ns

0.63ns

0.57ns

2.34

-0.11ns

1.85ns

-0.08ns

0.60ns

0.05ns

2.80

-0.41ns

3.41

-0.07ns

1.64ns

Self-search

-0.84

4.74

-0.11ns

11.96

-0.19ns

12.24

-0.39

14.37

-0.21

8.14

-0.14ns

8.24

-0.21

8.82

-0.22

5.43

-0.19

6.91

-0.30

6.70

No. of observations (chains)

21,581

7,319

12,782

15,202

17,939

10,482

21,597

5,826

13,680

15,283

18,763

10,582

22,074

6,001

14,595

15,191

19,670

10,424

22,597

5,810

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level

Probability changes calculated for the median observation using logistic regressions. 'Entered Last Mile' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. 'Reached Best Idea' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 25,000 runs for each landscape and ss-max condition. All runs used Small World II network, and parameters collab = 0.8 and recomb = 0.8.




Section 4: Supplementary Results by Environment                       

Section 4: Supplementary Results by Environment

Table OA4. Expected percentage point change in the probability of a given action chain reaching the last mile and developing into the best idea corresponding to one additional change activity, by Environment and ss-max.

Actor chooses max performing idea
(ss-max = TRUE)

Actor chooses better performing idea
(ss-max = FALSE)

collab = 0.3 & recomb = 0.3

collab = 0.3 & recomb = 0.8

collab = 0.8 & recomb = 0.3

collab = 0.8 & recomb = 0.8

collab = 0.3 & recomb = 0.3

collab = 0.3 & recomb = 0.8

collab = 0.8 & recomb = 0.3

collab = 0.8 & recomb = 0.8

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain activity

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

Within-network-community recombination

9.23

-6.58

4.08

-7.78

2.96

-11.71

1.94

-7.92

2.26

-11.17

1.98

-11.76

2.14

-4.35

0.61

-2.69

Between-network-community recombination

10.81

-5.14

3.98

-7.26

3.19

-12.49

2.66

-5.66

3.91

-9.07

2.02

-10.31

2.89

-5.70

1.10

-1.79

Within-network-community transfer

-0.01

1.55

-0.13

0.43

-0.07

1.84

-0.58

-0.03ns

-0.82

-1.16

-0.64

0.73ns

-0.25

-0.24

-0.41

0.56

Between-network-community transfer

-0.01

1.66

-0.12

0.90

0.07

6.68

0.21

3.53

-0.61

-0.28ns

-0.65

-0.79ns

0.01ns

3.05

-0.01ns

3.36

Self-search

-0.01

1.90

-0.19

1.19

-0.09

28.71

-1.21

16.77

-0.07

11.23

-0.27

11.07

0.23

9.78

-0.26

7.39

No. of observations (chains)

185,403

65,046

185,402

67,388

185,348

67,660

185,477

86,088

185,547

78,926

185,394

82,304

184,846

77,057

185,278

102,120

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level

Probability changes calculated for the median observation using logistic regressions. 'Entered Last Mile' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. 'Reached Best Idea' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 250,000 runs for each environment and ss-max condition (25,000 runs by landscape). All runs used network Small World II.




Section 5: Supplementary Results by Partner Selection Process

Section 5: Supplementary Results by Partner Selection Process

Table OA5. Expected percentage point change in the probability of a given action chain reaching the last mile and developing into the best idea corresponding to one additional change activity, by partner selection process.

Random partner selection

Performance based partner selection

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain acivity

(1)

(2)

(3)

(4)

Within-network-community recombination

1.79

-8.51

2.16

-9.70

Between-network-community recombination

2.29

-5.98

2.69

-5.96

Within-network-community transfer

-0.69

0.62ns

-0.54

-0.48ns

Between-network-community transfer

0.47

4.68

0.06ns

6.66

Self-search

-1.09

17.05

-0.96

17.72

No. of observations (chains)

37,029

17,273

37,002

16,513

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level.

'Performance based partner selection' results are based on a version of the model where ego only interacts with alters who are better performing. 'Random partner selection' results are equivalent to those presented in table 2 of the main paper, provided here for comparison purposes.

Probability changes calculated for the median observation using logistic regressions. 'Entered Last Mile' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. 'Reached Best Idea' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 50,000 runs for each Model version (5,000 runs by lanscape). All runs used Small World II network, and parameters collab = 0.8, recomb = 0.8 and ss-max = TRUE.

Section 6: Supplementary Results by Initial Condition                   

Section 6: Supplementary Results by Initial Condition

Table OA6. Expected percentage point change in the probability of a given action chain reaching the last mile and developing into the best idea corresponding to one additional change activity, by initial condition.

Actors starting outside the global basin

Actors starting at any location

Entered Last Mile

Reached Best Idea

Entered Last Mile

Reached Best Idea

Action chain acivity

(1)

(2)

(3)

(4)

Within-network-community recombination

1.79

-8.51

1.44

-6.00

Between-network-community recombination

2.29

-5.98

2.10

-3.51

Within-network-community transfer

-0.69

0.62ns

-0.40

-1.20

Between-network-community transfer

0.47

4.68

0.32ns

3.99

Self-search

-1.09

17.05

-0.89

16.96

No. of observations (chains)

37,029

17,273

36,596

17,769

Notes:

nsEstimated coefficients are not statistically significant at the 95% confidence level.

'Actors starting outside the global basin' results are equivalent to those presented in table 2 of the main paper, provided here for comparison purposes. In said model, the centroid for the network community could not be a location from which an actor could find the global peak through only self-search. 'Actors starting at any location' results are based on a version of the model that relaxes that restriction.

Probability changes calculated for the median observation using logistic regressions. 'Entered Last Mile' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach last mile and 0 if otherwise. 'Reached Best Idea' estimates are based on logistic estimation of a binary outcome: 1 if the action chain was the first in a given model run to reach the best possible discoverable idea and 0 if otherwise.

Estimations made using data from 50,000 runs for each Model version (5,000 runs by lanscape). All runs used Small World II network, and parameters collab = 0.8, recomb = 0.8 and ss-max = TRUE.